1. Field of the Invention
This invention relates generally to power transmissions and, more particularly, to a system and method for optimizing the life of power transmission components.
2. Description of the Related Art
The phenomenon of gear fatigue life is, by its nature, statistical. Two physical sources of fluctuation determine gear life—a random (rough) contact surface and defect dynamics under applied stress and thermal fluctuations. When two mating gear surfaces are placed into contact with each other under pressure, contact occurs at the points of asperities interactions, the result of which is local stress concentration at the junctions and lower stresses in other regions. Transient analyses of contacts, based on surface roughness profiles, are defined by profilometer traces, from which spectral characteristics may be obtained through Fourier transformation. Locally, damage accumulation is determined by defect concentration caused by the concentration of stress that plays the role of control parameter for defect nucleation and can be described by stress induced migration between multi-well free energy minima under the simultaneous thermal fluctuations that are proportional to temperature. Stochastic resonance theory and experimental results suggest that, when the Kramer's rate of escape from a free energy minimum has a value approximately equal to the periodic perturbation, in this case taken to be the periodic load or periodic stress due to machining features or other asperities, defect nucleation dramatically increases.
Sliding friction affects the gear tooth as an excitation. Sliding friction can be modeled as an external excitation with the same fundamental period as a gear surface profile. At high power operating gear mode, a lubricant film might be partially broken; under such circumstances, a regime of boundary lubrication is activated. Contact at asperities generates periodic force with a known spectral function. Also, each of the asperities contacts causes local asperity vibration, which in turn generates sound waves with specific frequencies within the subsurface layer. Micro-defects distributed within this layer have their own resonance frequencies. If these resonant frequencies are nearly equal, the process of damage accumulation significantly accelerates. As shown in FIGS. 3 and 4, stress intensity factors are maximized for wave numbers β=(ωa)/c belonging to the interval from β=1.3 to β=2; where ω is loading frequency and c is the speed of the elastic wave.
Accordingly, there is a need for systems and methods for optimizing power transmission component life, such as gear life. There is a further need for such systems and methods to utilize a surface having a distribution of asperities substantially outside of a resonance frequency of a gear subsurface layer. There is yet a further need for power transmission component life optimization that reduces damage from dynamic loadings, such as asperities collisions and asperities vibrations, by defining a corresponding surface profile.